In general, an intake air quantity of an internal combustion engine can be regulated with an intake pipe pressure. An intake pipe pressure is determined by a flow rate of air which passes through a throttle. A throttle passing flow rate is determined by a differential pressure of an upstream pressure and a downstream pressure of a throttle, and an opening (that is, an opening area) of the throttle. The physical model which is derived from such a relation is formula (1) described as follows. Formula (1) is a formula of throttling which shows a relation of a throttle passing flow rate mt, a throttle opening TA, a throttle upstream pressure Pac and a throttle downstream pressure Pm. K in formula (1) is a coefficient including a flow rate coefficient, B is an opening area at the time of the throttle opening being TA, φ is a function (pressure ratio term) of a pressure ratio Pm/Pac.
                              [                      Formula            ⁢                                                  ⁢            1                    ]                ⁢                                                                                                m          t                =                  K          *                      B            ⁡                          (              TA              )                                *                                    Φ              ⁡                              (                                                      P                    m                                                        P                                          a                      ⁢                                                                                          ⁢                      c                                                                      )                                      .                                              formula        ⁢                                  ⁢                  (          1          )                    
By modifying the above described formula of throttling, formula (2) described as follows can be obtained. According to the formula (2), the throttle opening TA which is a target can be calculated from the throttle passing flow rate mt and the pressure ratio Pm/Pac. The method which calculates a target throttle opening by calculation using such a physical model is a conventionally known method as is described in, for example, Japanese Patent Laid-Open No. 2007-205194.
                              [                      Formula            ⁢                                                  ⁢            2                    ]                ⁢                                                                                      TA        =                              B                          -              1                                ⁡                      (                                          m                t                                            K                *                                  Φ                  ⁡                                      (                                                                  P                        m                                            /                                              P                                                  a                          ⁢                                                                                                          ⁢                          c                                                                                      )                                                                        )                                              formula        ⁢                                  ⁢                  (          2          )                    
The calculation method of the target throttle opening using formula (2) also can be applied to an internal combustion engine with a supercharger. In this case, the pressure ratio Pm/Pac, which is one of parameters, is influenced by the throttle upstream pressure Pac which is determined by the rotational speed of a compressor, that is, a supercharging pressure. As a setting method of a supercharging pressure, there are several methods, and if the highest priority is given to fuel economy, the throttle is opened to be as close to full throttle as possible, and the supercharging pressure and the throttle downstream pressure, that is the intake pipe pressure, are preferably set to be substantially equal to each other.
However, in the situation in which the difference between the upstream pressure and the downstream pressure of the throttle is small, the throttle sometimes causes hunting when the supercharging state by the supercharger changes. This is because a relation as shown in FIG. 4 is established between the pressure ratio term φ and the pressure ratio Pm/Pac of formula (2). As shown in the drawing, in the region in which the differential pressure between the upstream pressure and the downstream pressure of the throttle is small, that is, in the region in which the value of the pressure ratio Pm/Pac is close to 1, the value of the pressure ratio term φ changes sharply with respect to a very small change of the pressure ratio Pm/Pac. As a result, the calculated value of the throttle opening oscillatorily changes, and hunting of the throttle occurs. Such hunting of a throttle can occur when the throttle is not opened close to full throttle. This is because since change of a supercharging pressure has a lag, the upstream pressure and the downstream pressure of the throttle sometimes become equal to each other transiently.